Question

consider a standard 52-card deck. if two jokers are added to this deck, how many 5-card hands can be dealt containing both jokers? you may use a calculator.

Answer 1

There can be 22,100 different 5-card hands dealt that contain both jokers when two jokers are added to a standard 52-card deck.

Step-by-step explanation:

To calculate how many 5-card hands can be dealt containing both jokers from a 52-card deck plus two jokers, we follow these steps:

1. First, we must place both jokers into our hand as they must be included.
2. There are now 3 remaining spots in our hand and 52 cards in the deck to choose from, since we've included the two jokers in the total count.
3. Therefore, we can use the combination formula, which is C(n, k) = n! / (k! * (n - k)!), where n is the number of items to choose from, k is how many to choose, and ! denotes factorial.
4. Plug the numbers into the formula: C(52, 3) = 52! / (3! * (52 - 3)!) = (52 * 51 * 50) / (3 * 2 * 1) = 22,100.

Thus, we can deal 22,100 different 5-card hands containing both jokers.